A new technique for curved rod bending tests based on digital image correlation

Abstract

Background. The study of the deformation of curved rods subjected to bending and its associated stress state is a complex task that has not been treated in depth in the literature, which makes difficult to obtain constitutive models or Finite Element Models (FEM) in which it is necessary to know all the components of the stress and strain tensors.

Objectives. This study focuses on a new calculation methodology to obtain stress and strain tensors of curved rods under bending.

Methods. The stress and strain tensors have been determined based on the theory of continuum mechanics and differential geometry of curves (moving bases), in a general methodology and valid for large strains, curved geometries and variable cross-sections along the specimen. This has been applied to the human rib and, in addition, a new experimental method for bending of curved specimens based on Digital Image Correlation (DIC) is presented.

Results. Both the test method and the proposed calculations applied to the human rib show results according to expectations, allowing to know the rib curvature changes along the test, the stresses and strains along the rib and the components of both stress and strain in all directions, in order to build the stress and strain tensors. In addition, the results of stress, strain and young’s modulus correspond to those of previous literature in tensile testing of human rib cortical bone.

Conclusions. The proposed calculations allow the construction of the strain and stress tensors of a curved specimen subjected to bending, which is of great importance for the development of constitutive models. Moreover, since with this method it is possible to calculate both tensors along the entire length of the specimen and in all directions, it is possible to apply this method in finite element models. Finally, the new test methodology allows to know the stress and strain in curved specimens such as the human rib, from bending tests.